Which produces more possible outcomes, a coin, or dice? The answer is dice.
Generally speaking, a coin has only two sides (the head and tail), but a dice has six (1 to 6). For a fair dice, each side has an equal possibility (one out of six) to show up.
However, for a biased dice, the probability of each side is not equal. For example, throwing a biased dice may always turn out to be one or two; the sides of three to six never appear. So a dice is not necessarily harder to guess than a coin if it is biased (e.g., only the “one” side always appears).
The key point of cryptography is the cryptographic key. If a key generator produces keys with few variations, it is more vulnerable. It is like a Ferrari racing car equipped with a 1200 CC engine. That is, a 256-bit key generator may only have the capability of generating 64 bits of combinations.
Entropy is the measure of the generator’s capability of randomness.
- The entropy of a fair coin is 1, based on the probability of 0.5 (head) and 0.5 (tail)
- The entropy of a fair dice is 2.58496, based on the probability of 1/6 for each side (1 to 6)
Which produces more possible outcomes, a coin, or dice? The answer is dice if both of them are fair.